## Introduction: Square Any 2-digit Number Ending in 5 Instantly and Easily.

This is a quick, easy math trick that gives you the square of any two-digit number ending in 5 (25 squared is 625; 85 squared is 7225, etc.).

You can go on to 'bump' the numbers higher or lower with simple arithmetic, if you wish.

## Step 1: Step 1. That's It. There's Just 1 Step

Let's use 35 squared as an example.

Take the "3" and add 1. That makes 4.

Multiply **3 times 4. That's 12**.

**Put "25" after the 12**. That makes 1225.

That's the answer. **35 times 35 is 1225**.

All you really had to do was add 1 and multiply.

**(OK, OK, it's really two or three steps. But they're pretty simple steps.)**

## Step 2: Expand on That Idea . . .

Let's say you need to know what 26 squared is.

That's the same as **25 squared, plus 25 (that's the same as 26 x 25), plus another 26 (that's 26 x 26)**.

So, 25 squared is 625, plus 25 is 650, plus 26 is 676. You should be able to do all this in your head.

Again, the reason you know 25 squared is 625 is because you strip off the leading 2, add 1 to it, and multiply those numbers by each other. 2 +1 = 3, then 2 x 3 = 6 and you just tack 25 on to the end.

Now you can quickly find how many combinations of letter pairs are in the alphabet. (26 times 26) is 676. If you drop the letter "i" because it's confused with the numeral "1" then you're back to 625. Drop the letter "O" because it looks like Zero, and you're using 625 - 25 (which is 24 times 25, or 600) and then subtract 24 more (because you're multiplying the 24 by 24 rather than 25), so you're at 600 minus 24 which is 576.

## Step 3: If You Want a Little Algebra . . .

There's an algebraic formula that proves why it works.

10x + 5 can describe a two-digit number ending in 5. In this case, let X = 2 so we can square 25

**(****10x + 5) times (10x + 5)**

can be factored as** (100x)squared + 50x + 50x + 25**** u**sing the FOIL method

Factoring and adding, we get (**100x times 100x) plus 100x plus 25**

Factoring, we get 100x squared plus 100x plus 25

Factoring, we get 100 (x squared plus x) plus 25

Factoring, 100 (**x** times (**x +1**)) plus 25 ----- in this example, x = 2 and x + 1 = 3

So, 2 times 3 (equals 6) times 100 (is 600) plus 25 is 625

75 squared is (7 times 8) which is 56 (hundred) plus 25 is 5625.

75 times 7**6** is 5625 plus 75 more (since we're multiplying it 7**6** times), or 5700

95 squared is (9 times 10 plus 25) or 9025

15 squared is 225

## Comments

3 years ago

This is a good trick!